The influence of the thickness of TiO 2 film on the performance of DSSCs

It is well known that the dye cells performance largely depends on the film thickness [40,188-190]. If d is considered as thickness of TiO2 film, its increase leads to increase dye adsorption and light absorption. This could have as consequence the increase in short-circuit photocurrent Jsc. High efficient DSSC require a TiO2 film thickness of d ~10 µm (excluding the scattering layer) with radius of nanoparticle ranging between 2-10 nm since with this thickness the light is entirely absorbed by the sensitzed TiO2 film [40].

The open-circuit voltage Voc of DSSC behaves complementary to Jsc. When the sensitized film thickness is increased a decrease in Voc is generally observed [188-190].

Gómez et al. found that by varying the film thickness between 3 µm and 9.7 µm the open-circuit voltage is decreased by ~0.06 mV. Chappel et al. [190] using SnO2 as inorganic semiconductor observed a decrease by 0.05V when thickness is changed from 0.1 µm to 4 µm. The open circuit voltage according to Ref. [188] was found to decrease by ~ 0.03 V when the TiO2 film thickness was increased from 5 µm to 11 µm.

However, it is worth noting that for a given photoelectrode, the optimal thickness depends on the extinction coefficient of the adsorbed dye as well as on the particle properties [40]. Ruthenium complexes dye with extinction coefficients lying in the range ε~10⁴ M^-1cm^-1 require thick nanoporous TiO2 film, whereas with metal free dye having generally high extinction coefficients (ε~10⁵ M^-1cm^-1) thin nanoporous TiO2 is expected. While the optimal

film thickness for N719 was reported [191] to be in the range of 10–15 µm, only 5 µm TiO2

film was reported to generate the best efficiency for hemicyanine dyes (metal-free dye) [192,193]. From these observations, it can be concluded that the ideal case in DSSC is to employ a dye that has a very high extinction coefficient on a very thin porous film, which can produce both high photocurrent and high photovoltage, resulting in a higher efficiency.

Perylene derivatives fit perfectly with these criteria.

In the experiments described here P1 was used as dye and a series of four devices with TiO2 thicknesses of 4, 7, 13 and 17µm were fabricated and characterized. Each device consisted of three identical cells showing same J-V characteristics. The electrolyte used consisted of 0.6 M 1-Butyl-3-methylimidazolium iodide, 0.1 M I2, 0.05 M LiClO4 in 3-methoxy-propionitrile. Figure 4.1 shows current-voltage characteristics of the corresponding devices and Figure 4.2 depicts the correlation between the thickness of TiO2 film and the parameters of the devices.

0,0 -0,2 -0,4 -0,6

0 2 4 6 8

Voltage / V

Current density / mA.cm-2 a)

4 µm TiO₂ 7 µm TiO₂ 13 µm TiO₂ 17 µm TiO₂

0,0 -0,1 -0,2 -0,3 -0,4 -0,5

-1,0 -0,8 -0,6 -0,4 -0,2 0,0

0,0 -0,1 -0,2 -0,3 -0,4 -0,5

b)

Current density / mA.cm-2

Voltage / V

4 µm TiO

2

7 µm TiO

2

13 µm TiO

2

17 µm TiO

2

Figure 4.1: Influence of TiO2 thickness on the performance of DSSC cells based on P1: (a) J-V characteristic of DSSC under simulated solar light AM 1.5 at 1 sun (100 mW cm^-2); (b) characteristics of DSSC in the dark.

2 4 6 8 10 12 14 16 18 20 340

360 380 400 420 440

0 2 4 6 8 Voc

a)

TiO2 thickness / µm

Jsc / mA cm-2

Voc / mV

J_sc

2 4 6 8 10 12 14 16 18 20

0.50 0.55 0.60 0.65 0.70

0.0 0.5 1.0 1.5 2.0 Fill Factor b)

TiO₂ thickness / µm

Efficiency / %

FF

efficiency

Figure 4.2: Variation of DSSCs parameters with TiO2 film thickness: (a) The empty (□) and the filled rectangular (■) makers show the Jsc and Voc, respectively; (b) The empty (○) and the filled circles (●) makers show the FF and efficiency η, respectively.

In principle, dye in the film will build up with increasing thickness, and an increased Jsc would be expected. However, from Figure 4.2(a) it can be seen that in DSSC assumption is valid just for thin TiO2 film. The short-circuit current density is increased from 2.69 mA cm^-2 to 6.98 mA cm^-2 when TiO2 film thickness is growing from 4 µm to 7 µm, respectively.

Beyond 7 µm the short-circuit current density decreases gradually to 3.39 mA cm^-2 for 13 µm and to 1.66 mA cm^-2 for 17 µm. This behavior is cleary illucidated in Figure 4.2 (a). That can suggest that, the probability of recombination and the cell resistance beyond 7 µm become large with increasing film thickness, since the electron has an average distance, to be transported across an increasing number of colloidal particles and grain boundaries. On the other hand, since the device is illuminated through the substrate, dye molecule adsorbed in the outer part (i.e part far from TCO glass) of TiO2 film will absorb less and less light with increasing film thickness as the dye adsorbed in the inner part (i.e the part adjacent to TCO glass) prevent a deeper penetration of the light.

At the same time the Voc decreases gradually from 427 mV to 403, 367 and 349 mV when the TiO2 film thickness is increased from 4, 7, 13 and 17 µm, respectively.

From Figure 4.2(b), it can be seen that the efficiency increases from 0.78% to 1.65% when the film thickness is changed from 4 µm to 7 µm and decreases gradually to 0.78% and 0.35% for film thickness 13 and 17 µm, repectively. The fill factor decreases from 0.675 to 0.588 when the film is changed from 4 to 7 µm (the minimum value was found at 7 µm), and increases slightly to 0.629 at 13 µm afterwards it remains almost unchanged at 17 µm. The FF of the cells shows about 25% decline as the thickness increases from 4 to 17 μm (Figure 4.2(b)),

which can be attributed to the increase of resistance in the cell [194]. This change in the property of DSSC with increasing thickness of a porous layer followed by the decrease of Voc

has already been mentioned in the literature and has been qualitatively discussed [188,190,194]. In fact Jsc grows with increasing d, but not proportional, since absorption by the Lambert-Beer's absorption law drops exponentially and thus the first few microns of sensitized TiO2 layer absorb a large part of the incident photons. The recombination process is expected to increase proportionally to d since both the TiO2/electrolyte-interface as well as the absolute number of surface states recombination is promoted proportionally with the increase of the layer thickness. The decrease in open circuit voltage when d is increased consequently results from a growing proportion of recombination site [195] contrasting with the slightly weaker increasing electron injection. This increases of electron injection and, thus, Jsc with layer thickness of TiO2 according to our results is observed in the range 4 µm < d < 7 µm. For d > 7 µm Jsc decreases gradually with the increase of d.

An expression of Voc describing quite perfectly its relation with the thickness of TiO2

film in the case of DSSC was reported [69,196] and is expressed by Eq. 4.1

0 0

ln ^ep

oc u m

et ox

A I V kT

qu n k c^α ϕ α

⎛ ⎞

= ⎜ ⎟

⎝ ⎠ 4.1

where α is the electron transfer coefficient, I0 incident photon flux, n0 the electron population in conduction band of TiO2 at the equilibrium, ϕep the ratio of injected electron toI0 , A the ratio of absorbed photon flux toI0, ket the rate constant for back reaction transfer. The order of the rate of reaction is expressed as the exponents m for the oxidized redox species and u for the electron respectively. Equation 4.1 describes a logarithmic dependence of the open circuit voltage on the incident light intensity, no distinction being made between free electrons in the conduction band and the localized electrons in surface states. The dependence of d is located in both the numerator and the denominator of the logarithmic expression. Assuming that the incident light I0 is constant, the absorption of photon increases with increasing film thickness and thus the number of injected electron in relation to the incident photons ϕep. The increase is, however, not linear, but proportional to (1 – e^-d) and goes at one hundred percent absorption in saturation [197]. In the logarithmic denominator of the Equation 4.1, the rate constant kr increases proportionally to TiO2 thickness and, hence, linearly to the surface states with d. Consequently, it is expected a decrease of the absolute value of the logarithmic expression of Equation 4.1 with d and hence the open circuit voltage Voc. This TiO2 thickness

dependence of Voc in DSSCs is quite similar to that reported in inorganic solar cells [198,199]

and is therefore considered as "normal". The use of thin silicon films was turned out to increase Voc in classical solar cell [200,201]. Queisser [199] gave a simple thermodynamic explanation for this change. He explained this behaviour by an entropy suppression in thin films. In inorganic solar cells, the confinement within a thinner layer of width W raises the density of carriers (per unit volume), higher density means reduced entropy, thus better conversion. From Eq. 3.3, considering the case of ideal diode (n = 1)

I

k T sc

Voc q ln Io 1

⎛ ⎞

≈ ⋅ ⎜ + ⎟

⎝ ⎠

4.2

where Isc is the short circuit current for V = 0.

The reverse saturation current is expressed as [199],

0 0

I q

τ

⋅ ⋅n W

= _4.3

being depending on carrier densities, no, lifetimes, τ, and transport parameters.

From Eq. 4.2 and 4.3 and with Isc << I0, one obtains the derivative, which is

oc k T

q V

d

dW W

= − ⋅

The entropy S per charge carrier particles in a semiconductor with an effective density of states Nc in the conduction band, having the electron effective mass m* [199,202], Nc = 2(2π m*kT/h²)^3/2 is [199,202,203]

c

5 ln

k 2 N (T)

S = − ⎛ n ⎞

⎜ ⎟

⎝ ⎠ ^4.4

The entropy S is the only physical quantity depending on W, since n(W) = Iscτ/qW.

Assuming that lifetime τ remains independent of thickness W and assuming non-degeneracy, and taking in account the extending of the Eq. 4.4 to hole p, one obtains [198]

oc k T d d

q d d

dV 1 1

d

n p

n p

W W W

⋅ − −

=⎛ ⎞⎛ + ⎞

⎜ ⎟

⎜ ⎟⎝ ⎠

⎝ ⎠ ^4.5

as the explicit formula for the change of output voltage with change of layer thickness W, based on the consideration of the entropy reduction with compression. Since the derivatives of particle densities with respect to thickness, such as dn/dW, are negative, the open-circuit voltage Voc does increase with shrinking W, and so does the efficiency, since the current remains constant.

The charge recombination in DSSC can be estimated by the magnitude and onset of the dark current, which arises from the reduction of I3− ions by the electrons in the conduction band. The dark current potential scans for photoelectrodes are plotted in Figure 4.1(b). The dark current onset is shifted to a lower potential with increasing thickness, and a thinner film produces a smaller dark current at the same potential above 0.25 V. These observations reflect a higher recombination rate between transported electrons and I3− ions in thicker films. The increase of the dark current with film thickness results in a loss in Voc. Thus, Voc decreases with increasing thickness [41].

From this investigation, a 7 µm thickness of TiO2 turned out to generate device with good performance. If not otherwise mentioned 7 µm is retained as thickness of TiO2 inDSCCs in this work, since all dye investigated have an extinction coefficient lying in the same range.

In the following sub-section the influence of electrolyte composition on the performance of DSSCs will be scrutinized.

4.1.2. The choice of the electrolyte: The influence of tBP and Lithium on the

Im Dokument Dye-sensitized solar cells based on perylene derivatives (Seite 66-71)